Johannes Kepler The German astronomer Johannes Kepler, b. Dec. 27, 1571, d. Nov. 15, 1630, was the first strong supporter of the heliocentric theory of Copernicus and the discoverer of the three laws of planetary motion. He attended seminaries at Adelberg and Maulbronn before studying theology, philosophy, and mathematics at the University of Tubingen. At Tubingen, Kepler's scientific ability attracted the notice of the astronomer Michael Maestlin. Through Maestlin, Kepler became a supporter of the Copernican theory, although his teacher continued to expound officially the old Ptolemaic system. Kepler had planned to enter religious life, but he accepted a chair in mathematics and astronomy at Graz. At the age of 24, Kepler published Mysterium cosmographicum (Cosmographic Mystery, 1596), in which he defended the Copernican theory and described his ideas on the structure of the planetary system. Influenced by the Pythagoreans, Kepler viewed the universe as being governed by geometric relationships that conform to the inscribed and circumscribed circles of the five regular polygons.

Although he was not a Copernican himself, Tycho Brahe, the mathematician at the court of Emperor Rudolph II at Prague, was so impressed with Kepler's work that in 1600 he invited Kepler to come to Prague as his assistant. Confronted with the Catholic persecution of the Protestant minority in Graz, Kepler gladly accepted. When Brahe died the following year, Kepler was appointed his successor and thus inherited Brahe's scientific legacy. This legacy included many accurate positional determinations of the planets, especially those of Mars. Kepler now embarked on an intensive study of the true orbits of the planets. Abandoning the ancient belief that the planets must move in perfect circles, Kepler concentrated on Mars. He proved that the orbit of Mars is an ellipse, with the Sun occupying one of its two foci. This, the first of Kepler's laws of planetary motion, appeared in Astronomia nova (New Astronomy) in 1609, with the second "law of areas" governing planetary velocity.

Always guided by the concept of beauty in the structure of the universe, and specifically by a theory of harmony in geometric figures, numbers, and music, Kepler, in his Harmonices mundi (Harmonies of the World, 1619), announced his third law--a relationship between the orbital periods and the distances of the planets from the Sun. His belief that the Sun regulates the velocity of the planets was a milestone in scientific thought, laying the foundation for Newton's theory of universal gravitation. Among Kepler's numerous scientific contributions are an influential treatise on the theory of optics (1604), a treatise on optics as applied to telescope lenses (1611), a work offering physical explanations of the appearance of a nova in 1604, and an enthusiastic acceptance of and elaboration on Galileo's observations with a telescope (1610). His Epitome astronomiae Copernicanae (Introduction to Copernican Astronomy, 1618-21) became one of the most widely read treatises on astronomy in Europe. Kepler's last great work, known as the Rudolphine Tables (1627), was a widely used compilation of accurate tables of planetary motion.

The posthumous Somnium (Dream, 1634), on which Kepler labored until shortly before his death, is indicative of his fertile mind. In this work, Kepler describes a journey to the Moon and discusses the existence of lunar inhabitants. A crucial link between the thought of Copernicus and that of Newton, Kepler was an important figure in the 17th-century scientific revolution. Johannes Kepler Biography Johannes Kepler Biography By Nola Taylor Redd, Space.com Contributor | May 21, 2012 09:03am ET MORE When Johannes Kepler was born in the late sixteenth century, scientists believed that planets in the solar system traveled in circular orbits around the Earth. The occasional problem was solved by the addition of miniature circles test — epicycles — to planetary paths. But Kepler not only adamantly defended the idea that planets orbit the sun, he also revealed that their paths were not perfect circles. His descriptions of planetary motions became known as Kepler’s laws.

[See also our overview of Famous Astronomers and great scientists from many fields who have contributed to the rich history of discoveries in astronomy.] Here is a brief biography of Kepler: German astronomer Johannes Kepler used mathematics to calculate the path of the planets, finding that they traveled not in circles, as long expected, but in ellipses. Credit: Johnnes Kepler Gesammelte Werke , C. H. Beck, 1937 Johannes Kepler Facts Born in December of 1571, young Kepler was a sickly child of poor parents. He was awarded a scholarship to the University of Tübingen, where he studied to become a Lutheran minister. While there, he studied the work of Nicolaus Copernicus , who taught that the planets orbited the sun rather than the Earth, though he had no observational evidence to offer as proof. In 1596, Kepler wrote the first public defense of the Copernican system.

This was a dangerous stance, given that in 1539, Martin Luther, founder of the Lutheran church, derided the theory when he first heard it, while the Catholic church deemed such a position heretical in 1615 (they later subjected astronomer Galileo Galilei to house arrest for his publication on the subject). In search of the most detailed notes about the paths of the planets , Kepler contacted astronomer Tycho Brahe. A wealthy Danish nobleman, Brahe built an observatory in Prague where he tracked the motions of the planets and maintained the most accurate observations of the solar system at the time. In 1600, Brahe invited Kepler to come work with him. Brahe, however, proved to be suspicious and unwilling to share his detailed notes with his assistant. Instead, he assigned Kepler to solve the mystery of Mars, one of the most puzzling problems in astronomy at the time. Ironically, the detailed records of the challenging planet were the tools Kepler needed to understand how the solar system functioned. When Brahe died in 1601, Kepler managed to acquire Brahe's observations before his family could use them to their financial benefit.

Kepler's laws The Martian problem, which Kepler said he would solve in eight days, took nearly eight years. Astronomers had long struggled to figure out why Mars appeared to walk backwards across the night sky. No model of the solar system — not even Copernicus' — could account for the retrograde motion. Using Brahe's detailed observations, Kepler realized that the planets traveled in "stretched out" circles known as ellipses. The sun didn't sit exactly at the center of their orbit, but instead lay off to the side, at one of the two points known as the focus. Some planets, such as Earth, had an orbit that was very close to a circle, but the orbit of Mars was one of the most eccentric, or widely stretched. The fact that planets travel on elliptical paths is known as Kepler's First Law. Mars appeared to move backward when Earth, on an inner orbit, came from behind the red planet, then caught up and passed it. Copernicus had suggested that observations made from a moving Earth (rather than a centrally located one) could be a cause of the retrograde motion, but the perfect circular orbits he posited still required epicycles to account for the paths of the planets.

Kepler realized that two planets, traveling on ellipses, would create the appearance of the red planet's backward motion in the night sky. Kepler also struggled with changes in the velocities of the planets. He realized that a planet moved slower when it was farther away from the sun than it did when nearby. Once he understood that planets traveled in ellipses, he determined that an invisible line connecting the sun to a planet covered an equal amount of area over the same amount of time. He posited this, his Second Law, along with his first, which he published in 1609. Kepler's Third Law was published a decade later, and recognized that the relationship between the period of two planets — the time they take to orbit the sun — is connected to their distance from the sun. Specifically, the square of the ratio of the period of two plants is equal to the cube of the ratio of their radius. While his first two laws focus on the specifics of a single planet's movement, his third is a comparison between the orbit of two planets. Other notable discoveries Though Kepler is best known for his defining laws regarding planetary motion, he made several other notable contributions to science.

He was the first to determine that refraction drives vision in the eye, and that using two eyes enables depth perception. He created eyeglasses for both near and farsightedness, and explained how a telescope worked. He described images and magnification, and understood the properties of reflection. Kepler claimed that gravity was caused by two bodies, rather than one, and as such, the moon was the cause of the motion of tides on the Earth. He suggested that the sun rotates, and created the word 'satellite'. He tried to use his knowledge of the distance Earth travels to measure the distance to the stars. Kepler also calculated the birth year of Christ. In recognition of his contribution to his our understanding of the motion of the planets, NASA named their planet-finding telescope after the German astronomer. Other references: Johannes Kepler Essay - Critical Essays - eNotes.com Johannes Kepler Essay - Critical Essays Johannes Kepler 1571–1630 German astronomer, essayist, and nonfiction writer. Kepler is regarded as a towering figure of the scientific renaissance and a seminal catalyst in bridging the medieval cosmology and the modern world-view.

Building on the heliocentric theory of the Polish astronomer Nicolaus Copernicus, Kepler established the three laws of planetary motion and corrected the central fault of Copemican astronomy, which had wrongly determined the orbital paths of the planets to be circular. Kepler described a universe in which planets spinning on their axis rotate around the sun in elliptical orbits and provided the mathematical equations to verify his premise. The new astronomy replaced the earth-centered Ptolemaic system that had prevailed since the second century. Utilizing the skillful observations of the Danish astronomer Tycho Brahe, Kepler was the first to demand irrefutable mathematical proof to validate his scientific theories. He is also considered the father of modern optics for first correctly describing both the physics and physiology of vision. He further utilized his optical knowledge in making important contributions to the design of the refracting telescope. His extensive work in mathematics led to the development of infinitesimal calculus. A deeply religious man, Kepler viewed the universe as the perfect creation of God, the prime mover and perfect geometrician. It was up to the scientist to unravel the natural laws of providential design.

But Kepler's insistence that all theories must be confirmed by precise, verifiable data made him a seminal figure in the development of empiricism and the scientific method. His groundbreaking theories and rigorous methodologies laid the path for Newtonian physics and the laws of universal gravity, which clearly marked the arrival of the modern era. Biographical Information Kepler was born at Weil der Stadt, Swabia in south-west Germany on December 27, 1571. His father, Heinrich, was a ne'er-do-well mercenary who often left his family for long periods before permanently abandoning them during Kepler's teen-age years. His mother Katharina was a meddlesome, disagreeable woman who was charged with being a witch in her later years. Kepler's childhood was unhappy and marked by recurring sickness, and it was apparent early on that he was ill suited for manual labor. His keen intelligence was noted, however, and he was the fortuitous beneficiary of a practice of the dukes of Württemberg that provided educational scholarships for intellectually gifted but impoverished students. Kepler attended several elementary and secondary schools where part of his early schooling stressed learning a very formal and ornate Latin writing style that would be reflected in Kepler's later writings.

He attended the Protestant University of Tübingen on scholarship, graduating in 1587. He continued his studies there and received his master's degree in 1591. Intending to enter the Lutheran ministry, Kepler pursed a curriculum in the arts. While at Tübingen he studied astronomy with Michael Maestlin who introduced him to both the Ptolemaic and Copernican systems. They began a friendship that would be of lasting importance throughout Kepler's life. Upon graduation Kepler began theological studies. But shortly before completing his course, Lutheran officials decided that Kepler's religious heterodoxy and refusal to sign the Formula of Concord made him an unsuitable candidate for the clergy. They recommended instead that he take a mathematics teaching post at a Protestant school at Graz in Austria. It was while giving a lecture one day that Kepler experienced a brilliant insight that explained the architectural order of the solar system. Kepler based his vision on what he believed to be an integral relationship between the six known planets and the five regular solids of Pythagorean mathematics.

Kepler published his theory in the Mysterium Cosmographicum (1596; Mystery of the Universe) when he was twenty-six and sent copies of his work to both Tycho Brahe and Galileo. Even though he rejected the thesis of Kepler's work, Tycho immediately recognized Kepler's brilliance and was especially impressed by his mathematical skills. When religious turmoil forced Kepler to leave Graz in 1600, he traveled to Prague to meet with Tycho who had just been appointed as the Imperial Mathematician by Emperor Rudolph II. Tycho had been working on his own theory of the universe which was a hybrid of the Ptolemaic and Copernican systems; the sun revolved around the Earth while all the other planets revolved around then sun. He invited Kepler to join him in his work in his observatory and to work particularly on determining the orbit of Mars. Expecting to be considered more as a colleague, the relationship was a bit strained when Tycho treated Kepler as a subordinate. The alliance had also been tested by the revelation of some old correspondence between Kepler and Nicolaus Raymarus Ursus who had also once served as Imperial Mathematician.

Their exchanges had begun in 1595 with a letter Kepler sent to Ursus praising him for his work. Tycho and Ursus were nemeses and rivals, the former having accused the latter of plagiarism. Brahe assigned Kepler the uncomfortable task of writing a major defense of his work against Ursus in which Kepler had to explain away his early correspondence as the fawning of a novice. Kepler and Tycho worked together, if a bit tenuously, for ten months before Tycho's unexpected death in 1601. Within two months Rudolph II named Kepler to the position of Imperial Mathematician. Besides formal scientific work Kepler's duties included providing astrological forecasts for the royal family. Kepler assumed numerous posts during his lifetime and the moves were generally precipitated by his having to leave an area due to reoccurring religious turmoil. A man of great faith, Kepler was nonetheless very tolerant of dissident views and his heterodoxy often placed him in disfavor with the authorities. The peaks and valleys that marked Kepler's professional life touched his personal life as well. In 1597 he married Barbara von Müller, a prosperous heiress, who at age twenty-three had already been widowed twice.

Though Kepler had initially been much in love with her, it soon became an unhappy marriage as Kepler found his wife to be undereducated and ill mannered, unable to comprehend or appreciate the importance of his work. Still the marriage endured for fourteen years until her death in 1611. Together they had five children of whom only two survived. She did not leave a will and Kepler was left virtually penniless. In 1612 Rudolph II was deposed and Kepler lost his post as Imperial Mathematician while increasing religious strife made it impossible for Lutherans to remain in Prague. Kepler moved to Linz and took the assignment of district mathematician. In 1613 Kepler wed Susanna Reutlinger, age twenty-four, who had been an orphan. It proved to be a much happier marriage and together they had seven children, but once again only two survived childhood. Beginning in 1615 Kepler's mother, still living in Württemberg, had become the subject of rumors involving sorcery. Kepler, living in Linz, became aware in 1617 of the seriousness of his mother's plight and became actively involved in her defense.

Although formally charged as a witch in 1621, she was eventually freed but died within several months of her release. Kepler's efforts on her behalf were partly motivated by filial duty and partly by self-defense. If his mother had been convicted both his mathematics career and personal safety would be imperiled. Still Kepler suffered more religious persecution during the Counter-Reformation and was forced once again to relinquish a job and leave his home. Beginning in 1628 Kepler spent the last years of his life studying and publishing at Zagao in Silesia under the patronage of Albrecht von Wallenstein, a duke and prosperous soldier of fortune. While traveling to Austria to collect a debt Kepler became ill and succumbed to fever at age fifty-nine at Regensburg, Germany on November 15, 1630. Major Works Kepler published The Mysterium Cosmographicum when he was twenty-six and the work reveals both the mystical and empirical elements in Kepler's intellectual orientation. Kepler posited that the five polyhedral shapes of Pythagorean mathematics were essential elements in the design of the universe.

In Kepler's Platonic vision, each of the five shapes fit nearly into the spaces between the orbits of the six known planets. Neptune, Uranus, and Pluto had yet to be discovered. While the first part of the book reveals Kepler's mystical orientation in suggesting that the geometrical perfection of the universe is the manifestation of a divinely inspired plan, the second half reflects Kepler's commitment to empiricism. He simply states that if observable and verifiable data cannot prove his theory, the thesis must be jettisoned. Astronomiae Pars Optica (1604; The Optical Part of Astronomy) contains Kepler's theories on how vision occurs through the process of refraction within the eye, discusses the development of glasses for both near sightedness and far sightedness, and explains how both eyes work together for depth perception. In the treatise Kepler also examines why the sun appears to vary in size at different times and discusses the creation of images using the pinhole camera. Astronomia Nova (1609; The New Astronomy) is Kepler's most important work and contains his first two laws on planetary motion. Tycho's observational data on Mars played a seminal role in Kepler's calculations.

Copernican cosmology was a highly complicated system that resembled clockwork architecture with complex orbits and epicycles that were not precise or provable. This work established Kepler's first two laws of planetary motion. The first law states that all planets travel on an elliptical orbit that has the sun as one point of its focus. The sun is off-center in the ellipse and a planet's distance from the sun varies according to where the planet is during its rotation. The second law postulates that the line connecting the sun and a planet will sweep through equal area in equal time regardless of where the planet is in its orbit. At the points when the planet is closer to the sun it travels faster; conversely, when a planet is farther from the sun the speed of its rotation is slower. But the area transversed in any period by a planet remains the same regardless of the speed at which the planet is traveling. Somnium Seu Astronomia (1634; A Dream of the Moon), Kepler's early experiment in writing science fiction, is the tale of an imaginary voyage to the moon. Although the story began circulating in manuscript form shortly after its completion in 1609, it was not published until after Kepler's death.

In Dioptrice (1611) Kepler discussed the refraction of the lens in human eyesight leading to the concept of the inverted telescope indispensable to astronomical observation. The Harmonice Mundi (1619; Harmony of the World) actually had its genesis as early as 1599 as Kepler sought to reconcile the natural harmony of the universe with the objectivity of scientific proof. This work contains Kepler's third law, which describes the relationship between planetary movements and their distances from the sun. His third law states that the cube of the average distance of each individual planet from the sun is proportional to the square of the time required for the planet to complete one full orbit. The treatise also contains elaborate musical equations and scales correlated with Pythagorean theory and to suggest the natural order, symmetry, and harmony of the universe. As a Platonist, Kepler sought to correlate musical forms with heavenly bodies as part of God's design for a flawless universe. In Epitome Astronomiae Copernicanae (1621; The Epitomy of Copernican Astronomy) Kepler established the true orbits of all the planets as well the satellites of Jupiter.

In the Tabulae Rudolphinae (1629; Rudolphine Tables), Kepler's last major work, he expanded on Tycho's observation and established in a comprehensive catalog of known celestial bodies the positions of the planets and of over 1000 stars. Besides major treatises Kepler's work also includes over 800 existing astrology forecasts done for himself, as part of his duties as Imperial Mathematician, and for wealthy patrons when financial need required him to do so. Critical Reception Kepler's scientific contemporaries immediately regarded his work as serious and important contributions to astronomy and cosmology, yet his writings were not widely disseminated for forty or fifty years after his death. But by the time Isaac Newton was building on Kepler's work, however, Kepler's theories were becoming increasingly known even in the popular culture. Critics have suggested that Kepler's highly formal Latin writing style made his work difficult to read in its original. He also had a habit of interjecting into his work all of his self-doubts suggesting where he may be in error—a practice that led to a very digressive writing style that many readers found tedious.

Kepler explained that these frequent sidebars were merely intended to provide guidance to future students and readers of his work, something he wished his scientific predecessors would have done. While newer data and observations have supplanted some of Kepler's theories and calculations, the bulk of his work remains accurate and applicable to modern physics, astronomy, optics, and mathematics. Much recent Kepler criticism focuses on the unique blend of mysticism and empiricism that is the hallmark of Kepler's vision. Start Free Trial Start your free trial with eNotes to access more than 30,000 study guides. Get help with any book. ESA Science & Technology: A History of Comets - Part 2 <br>Testing gravity: How comets helped to prove Newton right How comets helped to prove Newton right A History of Comets - Part 2 Testing gravity: How comets helped to prove Newton right In the seventeenth century, science was thriving across Europe. The concept of a heliocentric Solar System was slowly spreading, bringing with it a reignited curiosity for astronomy and a lessened fear of previously mysterious celestial objects, such as comets.

Cometary science was to take many great steps forward in the coming centuries – but first, comets had a vital part to play in developing one of the most fundamental theories in all of physics: Newton's law of universal gravitation. The Copernican system, by Andreas Cellarius. In public domain , via Wikimedia Commons The idea of a heliocentric system, proposed in 1543 by Polish astronomer Nicolaus Copernicus, was supported by the studies and observations of Italian astronomer Galileo Galilei, who first introduced the telescope to the practice of astronomy in 1609, and German astronomer Johannes Kepler, who formulated the laws of planetary motion between 1609 and 1619. This model firmly dismissed many older notions about the heavens; at the same time, the idea of comets being optical phenomena in Earth's atmosphere was also abandoned. Although comets had always been viewed as unwelcome omens connected to earthly events and catastrophes, firmly categorising them as celestial bodies unrelated to our planet weakened their reputation as portents of doom, slowly bringing them back into the realm of scientific investigation. On open-ended orbits Kepler observed several comets throughout his life, and tried to study their motion.

However, he believed comets to be interstellar objects moving along straight lines, and so never fully grasped their dynamics. Some progress on understanding cometary orbits came from Polish astronomer Johannes Hevelius, who observed nine comets and described them in his Cometographia treatise, published in 1668. Hevelius suggested that comets moved on open-ended parabolic orbits, meaning that they would be seen once and never again. This turned out to be partly true. Hevelius was on the right track, but a robust understanding of the orbital motion of comets would emerge only a couple of decades later, courtesy of English scientist Isaac Newton. The Great Comet of 1680 over the Dutch town of Alkmaar, in a painting by Lambert Doomer. Rijksmuseum, Amsterdam. In public domain Newton had been building on the work of Kepler and Galileo since the 1660s, finally announcing the results of his investigation into planetary orbits in 1687.

In fact, it was thanks to the encouragement – and economic support – of a friend and colleague that Newton eventually published his Philosophiae Naturalis Principia Mathematica, the pioneering text in which he detailed a theory of universal gravitation. This friend of Newton's was Edmond Halley - an English astronomer whose name is indelibly linked to comets. With his new theory at hand, Newton calculated the orbit of the Great Comet of 1680. His results were in excellent agreement with observations. Shortly after, Halley applied Newton's theory to the study of comets. This work would produce two major results: a striking confirmation of Newton's theory of universal gravitation, and a revolutionary change in our understanding of comets. The Great Comet of 1680, first comet orbit calculated using the theory of universal gravitation, by Sir Isaac Newton. In public domain , via Wikimedia Commons A predicted return Halley decided to use Newton's theory to calculate the orbits for several comets – some of which he had observed during his lifetime, and many more that he had retrieved from ancient records. In the process he noticed something strange: some comets seemed to have remarkably similar orbits.

He suspected that one comet in particular, which he saw in 1682, had already made an appearance once before, and was in fact the same one observed by Kepler in 1607 and by Apian in 1531. With this, Halley was the first to suggest that comets may be periodic, moving along very elongated ellipses rather than parabolic paths. He went so far as to forecast the comet's return. With an estimated period of about 76 years, Halley expected the comet to be visible again between the years of 1758 and 1759. Halley died before he could view it with his own eyes, but others were able to test and confirm his conjecture and, with it, Newton's theory of gravity. Interest in Halley's prediction spread to continental Europe. French mathematicians Alexis Clairaut, Joseph Lalande, and Nicole-Reine Lepaute spent several months performing detailed calculations on how the comet's path would be perturbed by various planets, working out its expected date of return and position in the sky.

Astronomers across Europe began looking for it as early as 1757, avidly stargazing until the long-sought-after comet was finally spotted again on 25 December 1758 by Johannes Palitzsch, a farmer from Germany. The sighting of this comet, which has since carried Halley's name, was a proof of Newton's theory of gravity, demonstrating that it can be applied not only to planets but to other celestial bodies too. It also marked one of the greatest triumphs of science: finally we understood how comets slotted into the cosmos, just as Seneca had hoped for many centuries earlier. Comets were no longer so unpredictable. As such, they started to be viewed as harmless, and slowly but surely popular prejudices and superstitions linked to comets began to fade away. Impacting science Although the nature of comets had been established, the investigation of these objects raised many new questions and opened up new disciplines of study. One avenue of investigation was the role of comets in Earth's history.

As increasing numbers of fossils were excavated from the depths of our planet, some scientists tried to explain their variety as having been caused by a series of short-lived, catastrophic events such as floods, volcanic eruptions, and cometary impacts. Others advocated a more uniform process, with gradual changes slowly taking place over millennia. Both interpretations eventually converged to form the currently dominating view of Earth's history as a slow, gradual process punctuated by occasional natural catastrophic events. Another field of study had its origins in an astronomical catalogue compiled by French astronomer Charles Messier in the 18th century. While scanning the sky in search of comets – and discovering thirteen new ones – Messier made an inventory of over a hundred blurry objects that he dubbed "nebulae". Originally intended as an aid for comet hunters such as himself, Messier's catalogue later became a very valuable database for astronomers with diverse research interests – his nebulae turned out to be stellar clusters, star-forming clouds, remnants of exploding stars, and even galaxies beyond our own. Although it seemed like our understanding of comets was becoming more complete, one vital piece was missing from this puzzle – we may have understood more about what comets are, but where do they come from?

What prompts these celestial bodies to appear in our skies? These questions were to be answered in the coming centuries by astronomers who revealed much about not only comets, but also about the Solar System's place in our Galaxy. Upper row: The globular cluster listed as M30 in Messier's catalogue, in a wide-field view from the Digitized Sky Survey (left) and as viewed in greater detail with the NASA/ESA Hubble Space Telescope (right). Lower row: The spiral galaxy listed as M83 in Messier's catalogue, in a wide-field view from the Digitized Sky Survey (left) and in a combined view from Hubble and the Giant Magellan Telescope (right). Credit: ESO and Digitized Sky Survey 2 (upper left); NASA/ESA (upper right); Digitized Sky Survey, STScI/AURA, Palomar/Caltech and UKSTU/AAO (lower left); NASA, ESA, and the Hubble Heritage Team (STScI/AURA) - Acknowledgment: W. Blair (STScI/JHU), Carnegie Institution of Washington (Las Campanas Observatory), and NOAO (lower right).

Kepler and the First Law of Planetary Motion Kepler and the First Law of Planetary Motion Jenny Hwang Johannes Kepler was an astronomer, mathematician, theologian and philosopher. His many achievements are commendable but it is one particular triumph which is familiar to many. That is the discovery of Kepler's Laws of Planetary Motion. I will concentrate on his first law: the orbits of the planets are ellipses with the sun at one focus. Kepler was born in Weil-der-Stadt, Germany in December 1571 to Heinrich Kepler and Katharina Guldenmann. His education started at the German Schreibschule in Leonberg, Germany as a result of his family's relocation. Later, he transferred to the Latin school, building a foundation for the language to be used in his future publications. In 1584, he entered the Adelburg Monastery school and Maulbronn, preparatory school for the University of Tübingen, in 1586. During his stay at Tübingen, Kepler was especially influenced by his professor of astronomy, Michael Mästlin.

Mästlin was a quiet proponent of Copernican astronomy, which supports the idea of a heliocentric (sun-centered) universe. His thorough knowledge of the ideas of Copernicus sparked Kepler's interest in astronomy and created another Copernican advocate. Ironically, Kepler was a reluctant astronomer. Of his interest in the subject, Kepler states, "these were prescribed studies and nothing indicated to me a particular bent for astronomy." Nevertheless, he was a "straight A student" and when he went to renew his scholarship at Tübingen, the senate spoke of Kepler as having "such a superior and magnificent mind that something special may be expected of him." [2] After receiving his masters degree from Tübingen in 1591, Kepler continued his studies in theology. But in his last year of courses, the professor of mathematics at the Lutheran school in Graz died and the University of Tübingen was asked to recommend a replacement. The school chose Kepler. Reluctantly, he abandoned his initial calling to be a clergyman and, at the age of 22, began his duties as a math instructor in Graz.

Just after a year of residency at Graz, Kepler published his first work, Mysterium cosmographicum (1596). In it, he presents his imaginative theories on the "secrets of the universe", the quest for which was inspired by his religious convictions. In the name of unveiling God's mathematical plan of the universe, Kepler concludes that the existance of six planets is due to the existance of five perfect polyhedrons. Of course this was based on the "fact" that there were only six planets in the universe and only five perfect polyhedrons. Around Earth's orbit, Kepler circumscribes a perfect dodecahedron and the sphere containing this is Mars' orbit. Similarly, around Mars' sphere, a tetrahedron is circumscribed and the sphere containing this is Jupiter's orbit. Inscribing an icosahedron in Earth's orbital sphere, the resulting inscribed sphere is Venus. This is done with the rest of the planets using the remainder of the perfect polyhedrons. Astonishingly, the ratios of adjacent planetary orbits represented in Kepler's nested spheres model coincides with Copernicus' calculations. Of course, Kepler relied mostly on divine inspiration for this theory.

There was no real basis for his argument. The importance of Mysteruim cosmographicum comes mostly from the fact that it was the first publicly Copernican treatise since Copernicus himself. Kepler was quite a revolutionary. Even his search for reasons why the planets moved the way they did was a bold endeavor, contrasting with the medieval tradition of simply accepting information without question. In September 1598, the Protestants in Graz, including Kepler, were ousted from the city by the Catholic rulers. Although Kepler was allowed to return, conditions were tense. Looking for relief, he turned to Tycho Brahe. Brahe, Imperial Mathematician for the Emperor Rudolph II and renowned for his impressive collection of planetary observations, knew of Kepler from Mysterium cosmographicum. When Kepler arrived at his Benatky Castle Observatory outside of Prague, in 1600, Brahe welcomed him as another aid to his own work, instead of an equal. A tumultuous relationship between them unsued until Brahe's death a year later. It was then that Brahe finally entrusted Kepler with his jealously guarded treasure of observations.

As a final request, Brahe relied upon Kepler to finish the Rudophine Tables of planetary motion. Two days later, Kepler was named Imperial Mathematician. Without his strenuous relationship with Brahe, Kepler was free to pursue his own areas of interest in astronomy. He decided to continue on his observation of Mars. Kepler was interested in documenting its orbit because he believed that if he could discover the particulartly confusing path of this planet it would be possible to uncover the orbits of all the other planets. Contrary to popular belief, he did not simply use Brahe's observations and pick a geometrical figure that fit the description. He was interested in discovering a "physical theory of planetary motion, from which the orbits could be deduced." [1] Before proceeding to explain Kepler's study of the orbits, a few astronomical terms should be clarified. eccentric circle: Planet, P, moves uniformily around a circle with center, C, which is eccentric to the sun, S. equant point: Introduced by Ptolemy, the planets do not move with uniform velocity but with constant angular velocity about another point, the equant point.

Thus, the planet, P, moves about the eccentric circle with uniform velocity about the equant point, E. According to Ptolemy, best approximation of the position of E was EC=CS (Figure A) [1]. aphelion: The point on the orbit where the planet is farthest from the sun. perihelion: The point on the orbit where the planet is closest to the sun. Kepler began his quest to understand the orbit of Mars by, first, describing Earth's orbit. After all, Mars was observed from a moving Earth. It was traditionally believed that the orbits were circlular and Kepler didn't stray from the idea for Earth's orbit. Also, he already noted that the linear speed of the planets decreased with distance from the sun in Mysterium cosmographicum and with Brahe's observations supporting the idea, Kepler incorporated the equant point in the orbit. He located the position of the equant point in relation to the center of the orbit and the position of the sun and concluded that Earth's velocity at aphelion and perihelion varied inversely with distance from the sun. This relation was generalized for the rest of the orbit (which was false) and was labeled the distance law.

Without the conveniences of calculus available to him, Kepler expressed this relation as: Where is called the eccentric anomaly, t is time, is the distance for eccentric anomaly i, and i is measured (Figure B) . This calculation is, no doubt a tedious task. Therefore, Kepler opted to approximate the distance value using area. This approximation proved to be reliable in predicting the positions of the Earth. Thus, the planet sweeps out equal areas at equal times. The relation was: [1] With Earth's orbit defined (it's orbit is very close to a circle so Kepler's model fit with observed data), Kepler moved on to Mars. Again, he started with a circular orbit but when the area law was applied to this model, Kepler found that his model produced discrepancies of up to 8'. At degrees, the error was +8'. At , the error was -8'. This meant that the planet on Kepler's model was moving too quickly at aphelion and perihelion and too slowly at the sides ( or ) (Figure C) . To resolve this, Kepler decided to change the shape of the orbit. Bringing the sides of the orbit inside the circle would result in a more accurate representation of Mars' actual position.

Indeed, further investigation on the position of Mars at different times of the year confirmed that its orbit did bow in from a circle. Thus, Kepler felt justified in making the change. The orbit that followed was more similar to the shape of an oval. But how could Kepler use the area law on this strange shape? For purposes of calculation, he chose to approximate the oval by an ellipse. The area law could be applied to an ellipse because the areas of ellipse sectors were known through the work of Archimedes. Through trial and error, Kepler found that making the semi-minor axis and the semi-major axis equal to 1 was the correct ellipse (where e is the distance CS. Inscribing the ellipse in the unit circle (Figure D) : Given: PC=1. For , the angle between PC and PS. Thus, Then, Kepler became inspired. What if this relation were true for all angles, ? Then, for any angle, , between CA and CP, the ratio of the distance, SP, to the actual sun-Mars distance would equal the ratio of SP with the perpendicular projection, PT, on a diameter of the circle. Thus, the sun-Mars distance=PT=PC+CT (Figure E) .

So, sun-Mars distance= . Knowing this distance, how was it to be portrayed in the orbital model? At first, Kepler decided to place Mars at point Q ,in Figure E, on the radius of the eccentric anomaly. So, the distance would have to correspond to the line connecting the sun to a point on the eccentric anomaly, Q. However, this was false. The curve traced out did not agree with observation. There were errors of up to 8'. Finally, Kepler discovered that the distance, , should apply to the segment connecting the sun with the point, W, on the line perpendicular to CA (Figure F) . The curve traced by this model was an ellipse and it predicted the correct positions of Mars. Consequently, Kepler accepted this ellipse, a shape initially used for approximation, as the true orbit of Mars. Also, Kepler was able to prove that the orbit traced out was an ellipse. KEPLER'S PROOF: Given an ellipse with center= , where e=CS, let v= the angle subtended by the arc, WA then, and .

Squaring and adding both equations: (neglecting the term in ) Thus, the ellipse can be written as , which is also the value that Kepler worked out before from his orbital model. Of course to work out the location of the focus: (neglecting the term in ) Thus, c=e, which is precisely the distance of the sun from the center in Kepler's model. Therefore, the sun is at one focus and Kepler's first law of planetary motion was born. After eight years of calculations, Kepler's first law of planetary motion was incorporated into the Astronomia nova, along with his second law: a planet sweeps out equal areas in equal times, which was mentioned earlier. Kepler's third law, dealing with the ratios of periods of planetary orbits appears in Harmonice mundi, although it is not stated as clearly as the other two laws. The astronomer also published several minor works, including Stereometria doliorum vinariorum, considered to be a significant work in the prehistory of calculus. Epitome astronomiae Copernicanae is also worth mentioning. It is an eight volume collection on Kepler's heliocentric astronomy and includes his three laws of planetary motion.

The Tabulae Rudolphinae that Brahe had wanted Kepler to work on was finally published in 1627. It was a table of planetary positions far more accurate than any other consisting of 119 pages of tables. Besides planetary observation, there were other subjects that entertained Kepler. He took an interest in optics and was noted, by Descartes, as being the most knowledgable of his time on the subject. Even Galileo looked towards Kepler for approval of his publications [2]. Another of Kepler's publications concentrates on the hexagonal trait of snowflakes. Although he disparaged its practice, Kepler also participated in astrological prognostications. He published several calendars while in Graz and Prague with enough accuracy to earn him some early fame. It also provided income when Kepler's financial situation was less than favorable. Despite his success, Kepler was continually plagued with financial trouble. The turbulance of the times and Kepler's constant relocation, in search of religious tolerance, contributed to positions with witheld income. Several times, he tried to secure a teaching position at Tübingen but, he was perceived as a renegade by fellow Protestants and refused.

Johannes Kepler died on November 15, 1630. He was on his way to collecting his backpay when stricken by an acute fever and was buried in a Protestant cemetary. Kepler's epitaph as noted by his son-in-law: Mensus eram coelos, nunc terrae metior umbras: Mens coelestis erat, corporis umbra jacet. I used to measure the heavens, now I shall measure the shadows of the earth. Although my soul was from heaven, the shadow of my body lies here. BIBLIOGRAPHY 1. Aiton, Eric J, How Kepler Discovered the Elliptical Orbit, The Mathematical Gazette, v.59, 1975 2. Gillispie, Charles Coulston, Dictionary of Scientific Biography, v.7, Charles Scribner's Sons, New York, 1981 3. Katz, Victor J, A History of Mathematics, Addison-Wesley, 1998 4. Kepler, Johannes, Astronomia nova, Heidelberg, 1609 5.

Kepler, Johannes, Harmonice mundi, Linz, 1618 6. Kepler, Johannes, Mysterium cosmographicum, Graz, 1596 7. Kepler, Johannes, New Astronomy, translated by Donahue, William H, Cambridge University Press, Great Britain, 1992 8. Wilson, Curtis, How Did Kepler Discover His First Two Laws?, Scientific American, v.226, 1972 Johannes Kepler Johannes Kepler developer of three laws of planetary motion Johannes Kepler was born on December 27, 1571, in Weil (near Stuttgart), Germany. It was while studying theology and the classics at the University of Tï¿½bingen that he learned about the heliocentric theory of planetary motion first developed by Nicolaus Copernicus . From 1594 to 1600, he held the chair of astronomy and mathematics at the University of Graz, Austria. While at Graz, Kepler worked out a complex geometric hypothesis to account for distances between the planetary orbits. He then proposed that the Sun emits a force that diminishes inversely with distance and pushes the planets around in their orbits.

He published his account in a treatise entitled Mysterium Cosmographicum (Cosmographic Mystery) in 1596. Kepler left Graz in 1597 rather than undergo compulsory conversion to Roman Catholicism. While seeking another post, he became assistant to the Danish astronomer Tycho Brahe in the latter's observatory near Prague. On the death of Brahe in 1601, Rudolph II, the Holy Roman Emperor, appointed Kepler to be Brahe's successor as imperial mathematician. Kepler made his most significant discoveries when he tried to find an orbit to fit Brahe's observations of Mars . Earlier astronomers believed a planet's orbit was a circle or a combination of circles, but Kepler could not find a circular arrangement to agree with Brahe's observations. He realized that the orbit could not be circular, and resorted to an ellipse in his calculations. The ellipse worked, and Kepler destroyed a 2,000-year-old belief.

In 1609, he published Astronomia Nova (New Astronomy), which contains two of his laws of planetary motion: (1) every planet follows an oval-shaped path around the Sun, called an ellipse, with the Sun at one focus; and (2) an imaginary line from the center of the Sun to the center of a planet sweeps out the same area in a given time, meaning that planets move faster when they are closer to the Sun. Right: the apparent movements of the then-known planets as observed from the Earth. In 1612, Kepler became mathematician to the states of Oberï¿½sterreich (Upper Austria). In 1619, while living in Linz, he published his Harmonica Mundi (Harmony of the World), the final section of which contains his third law of planetary motion: (3) the ratio of the cube of a planet's distance from the Sun and the square of the planet's orbital period is a constant and is the same for all planets.

Epitome Astronomiae Copernicanae (Epitome of Copernican Astronomy), published between 1618 and 1621, brought all of Kepler's discoveries together in a single volume, and became the first textbook of astronomy to be based on Copernican principles. Tabulae Rudolfinae (Rudolfine Tables), published in 1625, consists of new tables of planetary motion based on Brahe's data. Kepler also founded modern optics by giving the earliest acurate account of the way in which the human eye works. He correctly identified the pupil as a diaphragm through which light rays enter the eye and described the way in which they are refracted. He suggested that people with blurred vision had an optical defect which meant that rays were focused either in front of or just behind their retina. He then went on explain how telescopes work by refracting light and brining an enlarged image to focus in the eyepiece. His work provided the theoretical basis for subsequent improvements in telescope design and for the development of opthalmic optics as a recognized branch of medicine. Johannes Kepler died in Regensburg, on November 15, 1630. The Galileo Project

Question: Which scientist first described the laws of planetary motion between 1609 - 1612?
Answer: Johannes Kepler